The deal is worth $49 million-plus, a source confirmed to ESPN The Magazine's Chris Broussard.
Incentives could push the total financial package to well more than $50 million, the source said.
"Utah has become my home and I am excited to be able to continue my career playing for the Jazz and the best fans in the NBA," Favors said in a statement.
Yahoo! Sports earlier reported terms of the deal.
The 6-foot-10, 263-pound Favors is expected to start for a Jazz team that lost Al Jefferson and Paul Millsap during the offseason. The 22-year-old primarily came off the bench last season for Utah, averaging 9.4 points, 7.1 rebounds and 1.7 assists in 23.2 minutes per game.
"We have tremendous respect for and confidence in Derrick and see him as an important part of our future. He brings a toughness and defensive mindset that make him a key piece to what we are trying to build here," Utah general manager Dennis Lindsey said in a statement released by the team. "Derrick is also a high-character individual and he has shown a dedication to continue to improve all aspects of his game."
Originally selected third overall by New Jersey in 2010, the former Georgia Tech standout was part of the February 2011 deal that shipped star point guard Deron Williams from the Jazz to the Nets.
Favors would have become a restricted free agent after this season if he and the Jazz hadn't reached an extension deal by the Oct. 31 deadline.
Information from The Associated Press was used in this report.